A surface is tame if its complement is -ULC

Author:
R. H. Bing

Journal:
Trans. Amer. Math. Soc. **101** (1961), 294-305

MSC:
Primary 54.75

MathSciNet review:
0131265

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References | Similar Articles | Additional Information

**[1]**J. W. Alexander,*An example of a simply connected surface bounding a region which is not simply connected*, Proc. Nat. Acad. Sci. U.S.A. vol. 10 (1924) pp. 8-10.**[2]**R. H. Bing,*Locally tame sets are tame*, Ann. of Math. (2)**59**(1954), 145–158. MR**0061377****[3]**-,*Approximating surfaces with polyhedral ones*, Ann. of Math. vol. 61 (1957) pp. 456-483.**[4]**R. H. Bing,*An alternative proof that 3-manifolds can be triangulated*, Ann. of Math. (2)**69**(1959), 37–65. MR**0100841****[5]**R. H. Bing,*Conditions under which a surface in 𝐸³ is tame*, Fund. Math.**47**(1959), 105–139. MR**0107229****[6]**-,*A wild sphere each of whose arcs is tame*, Duke Math. J.**[7]**-,*Side approximations of*2-*spheres*, submitted to Annals of Math.**[8]**Ralph H. Fox and Emil Artin,*Some wild cells and spheres in three-dimensional space*, Ann. of Math. (2)**49**(1948), 979–990. MR**0027512****[9]**Edwin E. Moise,*Affine structures in 3-manifolds. IV. Piecewise linear approximations of homeomorphisms*, Ann. of Math. (2)**55**(1952), 215–222. MR**0046644****[10]**Edwin E. Moise,*Affine structures in 3-manifolds. VIII. Invariance of the knot-types; local tame imbedding*, Ann. of Math. (2)**59**(1954), 159–170. MR**0061822****[11]**C. D. Papakyriakopoulos,*On Dehn’s lemma and the asphericity of knots*, Ann. of Math. (2)**66**(1957), 1–26. MR**0090053****[12]**John R. Stallings,*Uncountably many wild disks*, Ann. of Math. (2)**71**(1960), 185–186. MR**0111003**

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DOI:
https://doi.org/10.1090/S0002-9947-1961-0131265-1

Article copyright:
© Copyright 1961
American Mathematical Society